Activity-Conditioned Residual Association from Aggregated Relational Data

Abstract

Aggregated relational data (ARD) record how many ties sampled respondents have to prespecified groups without revealing individual dyads. We develop a conditional test for prespecified cross-group concordance beyond an additive-activity network model. When the groups form an exhaustive partition, respondent degree is observed exactly. For arbitrary fixed activity values under an independent-Bernoulli additive-logit null, conditioning two respondents on equal degree yields a finite nonpositive sign restriction for their two disjoint group-count differences. Analyst-randomized pair thinning gives a conservative baseline. Under a stronger fixed-cell design with group-specific smooth activity profiles and positive cross-role overlap, an observable clipped full-pair statistic gives conservative one-network inference with graph-independent sampled respondents. Finite and growing matched-law constructions establish that the target contains bivariate information absent from a collapsed binary count. The full-pair procedure is uniformly consistent on a primitive relative-open neighborhood of a specified rank-one alternative. Fixed-dimensional lattice local limits make the conditioning and availability requirements explicit.

40 pages, 2 tables. Expanded version with full-pair inference, complete proofs, and additional numerical evidence